Keep secret identity when entertained by the fellow (4)
I believe the answer is:
hide
'keep secret' is the definition.
(thesaurus)
'identity when entertained by the fellow' is the wordplay.
'identity' becomes 'id' (I've seen this in other clues).
'when entertained by' means one lot of letters goes inside another.
'the fellow' becomes 'he' (I've seen this in other clues).
'id' put inside 'he' is 'HIDE'.
(Other definitions for hide that I've seen before include "(Place of) conceal(ment)" , "Tanned skin of an animal" , "Secrete - animal skin" , "Not show" , "Keep under wraps" .)